The theoretical statistics major provides the mathematical underpinnings of modern statistical practices of estimation, inference and prediction. The major explores both classical approaches to estimation and testing, such as maximum likelihood and the frequentist approach, as well as Bayesian methods that have become ubiquitous parts of modern data analysis. The major covers the theory needed to understand statistical modelling through a variety of lenses: parametric, non-parametric, large-sample theory, small-sample behavior, robustness, and the use of prior information.

## Learning Outcomes

Explain the notion of a parametric model, point estimation of the parameters of those models, including maximum likelihood estimation, and inference in simple statistical models with several parameters.

Demonstrate an understanding of approaches to include a measure of accuracy for estimation procedures and our confidence in them, and apply them to interval estimation.

Demonstrate an understanding of and apply methods of hypothesis testing to assess the plausibility of pre-specified ideas about the parameters of a model.

Explain and apply the ideas of non-parametric statistics, wherein estimation and analysis techniques are developed that are not heavily dependent on the specification of an underlying parametric model.

Demonstrate an understanding of the basic concepts of robust estimation in statistics, be able to derive influence functions of simple estimators and use them to evaluate the robustness of estimators.

Demonstrate an understanding of and explain the different uses of randomisation in statistics.

Develop, describe analytically and implement common probability models in the Bayesian framework, interpret the results of a Bayesian analysis and perform Bayesian model evaluation and assessment.

Demonstrate an understanding of the role of the prior distribution in Bayesian inference, and in particular the use of non-informative priors and conjugate priors.

Fit hierarchical models and provide the technical specifications for such models.

Demonstrate an understanding of various important concepts in forecasting and different approaches for modelling trend, seasonality and persistence.

Tailor-make models for specific applications and use them to produce forecasts.

## Other Information

Students will need to complete all of the following courses in order to be able to complete the 48 units of this major:

- MATH1013 OR MATH1115 OR MATH1113
- MATH1014 OR MATH1116 (only required if MATH1113 not completed)
- STAT1003 OR STAT1008 (may be included in the 18 units from completion of further courses from the subject area STAT Statistics)
- STAT2001 OR STAT2013 (may be included in the 18 units from completion of further courses from the subject area STAT Statistics)
- STAT2008 OR STAT2014 (may be included in the 18 units from completion of further courses from the subject area STAT Statistics)

## Relevant Degrees

## Requirements

This major requires the completion of 48 units, which must include:

24 units from completion of the following compulsory courses:

EMET3007 Business and Economic Forecasting

STAT3013 Statistical Inference

STAT3016 Introduction to Bayesian Data Analysis

STAT3056 Advanced Mathematical Statistics

6 units from completion of 2000-level courses from the subject area MATH Mathematics

18 units from completion of further courses from the subject area STAT Statistics

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